The present invention is germane to the propagation of polarization entangled photon pairs collinearly incident upon a modified hyperspectral birefringent filter stage and routed intact into two possible directions upon exit from the filter. Polarization entanglement is preserved.
Referring to FIG. 1, a previous similar effort, specifically the hyperspectral filter 30, was designed by Optical Physics Company and constructed under an AFRL Small Business Innovative Research (SBIR) contract award, and was solely intended as a network “hub” residing in a geostationary or geosynchronous orbit. Its mission is to support low probability of detection, interception, and exploitation links at very high data rates simultaneously to several users nearer to or on earth over a geographical region roughly the size of the Midwest United States. Such users will henceforth be referred to as “spokes.” A hub and spoke network configuration, electromagnetic beams transporting information between the spokes near earth and the hub at geo orbit are comprised of many photons, say in the 1550 nm band. They are classical electromagnetic beams, fully describable by classical electrodynamics.
As previously mentioned, an existing patented birefringent spectral filter stage, U.S. Pat. No. 7,400,448, was awarded to Richard Hutchins, Optical Physics Company [1] and manifested in SBIR contract FA8750-11-C-0163. It is intended for securing free space laser communications applications where robust wide angle acceptance in both azimuth and elevation is required. In U.S. Pat. No. 7,400,448, optical signals from the spokes are assigned distinct frequencies in the telecom band and possess common incident polarizations oriented 45° with respect to the optical axis of a set of birefringent spectral plates. A birefringent filter stage 10 is comprised of the birefringent plates, called a Lyot filter or birefringent stack, (also referred to as birefringent filter stack or filter stack) 10, followed by a polarization beam splitter 20, as shown in FIG. 1. The polarization beam splitter's 20 plane of incidence is oriented 45° with respect to the birefringent stack 10. It is therefore oriented in concert with the incident beams.
The primary contribution of U.S. Pat. No. 7,400,448 to OPC was to find an innovative way to increase the angular acceptance for simultaneous, multi-access laser communications employing wavelength division multiplexing to distinguish distinct, spatially displaced users. U.S. Pat. No. 7,400,448 incorporates a broadband half-wave plate between two birefringent plates whose extraordinary axes are perpendicular to one another and to the propagation direction of the laser light. Incoming frequencies whose optical path difference phase over the Lyot filter stack is an even integral multiple of π will suffer no polarization change in transit through the filter. We call these frequencies congruent. However, incoming frequencies whose optical path difference phase is an odd multiple of π will suffer polarization rotations by 90°. We call these frequencies incongruent. Incoming congruent and incongruent beams are split into orthogonal directions at a polarization beam splitter, or PBS. Thus, the hyperspectral Lyot filter stack prepares incoming beams for spatial separation by the PBS, accomplishing wavelength division multiplexing for classical laser beams. Those classical laser beams initially possess common polarizations preset to be 45° with respect to the Lyot filter reference frame. Their polarizations are, however, coincident with the PBS frame which is oriented 45° with respect to the Lyot filter frame of reference. After exiting the Lyot filter stack, one set of beams, say the congruent set, possess polarizations orthogonal to the PBS plane of incidence; they reflect from the splitting surface. Incongruent beams possess polarizations parallel to the PBS plane of incidence and transmit through the splitter interface.
Another feature of U.S. Pat. No. 7,400,448 is the incorporation of moveable wedges which can tune the optical thickness of the birefringent wedges to select desired transmission frequencies. This is the primary application U.S. Pat. No. 8,427,769 to Raytheon employs in their Lyot filter tuning device. U.S. Pat. No. 8,427,769 accomplishes a very fine frequency tuning of a laser beam by passing the beam multiple times through the tunable aspect of the wedges deployed in one aspect of the U.S. Pat. No. 7,400,448 to OPC Lyot filter, where again, OPC's filter is not critical to the U.S. Pat. No. 8,427,769 to Raytheon application. It is simply one medium to accomplish one function the multi-pass Raytheon patent employs to tune a laser beam to a desired frequency. The present invention could perhaps utilize this capability for future use, but is not compatible with the present invention at this time because the present invention instead switches the routing by adjusting the incoming frequencies for a given static Lyot stack thickness, and thus achieving its goal of preserving the polarization entanglement.
Still referring to FIG. 1, distinct input frequencies from the distant spokes are either congruent or incongruent with respect to the filter stack 10. In traversing the filter stack 10, polarization states of congruent frequencies are not rotated, while polarization states of incongruent frequencies are rotated by 90°. The two polarization states possessed by each beam exiting a filter stack 10 are either transmitted or reflected at the splitting interface within the polarization beam splitter 20. In other words the filter stack 10 prepares incoming beams for splitting into orthogonal directions by the polarization beam splitter 20, thus enabling wavelength division multiplexing (WDM) for simultaneous access between the network “hub” and its spatially distributed “spokes.” Moreover, if classical beams comprising a sum of vertical and horizontal polarized states containing many photons of two distinct frequencies are propagating along a line and entering the hyperspectral filter stage 30, one will measure both horizontal and vertical polarized states exiting the beam splitter at both output ports. The beams are a sum of electric field amplitudes comprising many photons. An entangled photon pair state is different; beams are divisible, single photons are not. Yet a pair of single photons generated by interactions at their source, such as four wave mixing in an optical fiber pumped by a sufficiently intense laser pulse, can possess two possible polarization states. They are either both horizontally polarized along the same coordinate axis, or they are both vertically polarized along an orthogonal axis. Both such possibilities are equally probable, but the state is unknown until measurement. Their joint probability quantum amplitude is expressed as a sum of product probability amplitudes,
                                                                    Γ              ⁡                              (                                                      f                    1                                    ;                                      f                    2                                                  )                                      〉                    in                =                              1                          2                                ⁢                      (                                                                                                f                    1                                    ,                                      H                    1                                    ,                                                            P                      1                                        ;                                          f                      2                                                        ,                                      H                    2                                    ,                                      P                    1                                                  〉                            +                                                                                    f                    1                                    ,                                      V                    1                                    ,                                                            P                      1                                        ;                                          f                      2                                                        ,                                      V                    2                                    ,                                      P                    1                                                  〉                                      )                                              (        1        )            Equation (1) expresses the input quantum state as a collinearv entangled photon pair prior to entering the hyperspectral filter stage 30 at P1. The term on the left of the plus sign is the probability amplitude that the joint state contains two photons, one with congruent frequency, f1, and one with incongruent frequency, f2. Both are horizontally polarized, and both are incident on port P1 in FIG. 1. The term on the right of the plus sign is the probability amplitude that the joint state contains two photons, one with congruent frequency, f1, and one with incongruent frequency, f2. Both are vertically polarized, and both are collinearly incident on port P1 in FIG. 1. The probability of measuring the product state on the left is the square of the coefficient multiplying it, here equal to ½. Similarly, the probability of measuring the product state on the right is ½.
Polarization measurement entails projection of the state onto detectors wherein the photon's energy is converted into an electrical signal; the photon is destroyed, its energy converted to electricity. In such a process, measurement of horizontal polarization of one photon necessitates horizontal polarization of the other. The measurements are 100% correlated. Likewise, vertical polarization measured on one photon necessitates vertical polarization on the other. Again, measurements are 100% correlated. Either possible outcome of a polarization measurement on the two photons occurs at random and, as stated above, equally probable. In no case is horizontal polarization measured on one photon and vertical polarization measured on the other. These correlations arise from conservation of energy and angular momentum at the source of the photons, and subsequent engineered assurance that both possibilities exist until measurement of the initial state, i.e., by entangling the two possibilities. Assigning logic bit 1 to horizontal polarization and logic bit 0 to vertical polarization, polarization measurements on the entangled state generates a random bit stream, useful for cryptographic purposes and quantum information processing applications. In other words, an entangled polarization state can be a carrier of random numbers which can be securely shared between two parties.
It is important to note that if the photons are split into two distinct directions as a function of frequency, and their polarizations are measured in two non-orthogonal two dimensional bases oriented relative to one another by 45°, ambiguity is imparted to the value of a logic bit when the two polarization bases are different. For example, in a quantum key distribution protocol application where legitimate users share common knowledge of which basis is used in every transmission between them, security is enhanced under intercept and resend attacks by an eavesdropper who does not share the common basis choice. Eavesdroppers will be wrong a discernable fraction of the time, alerting legitimate users of their intrusion. This added security measure is not present in utilization of the frequency for secret key generation in the state given by equation (1).
Frequency measurements of the initial state in equation (1) are not random. They occur in either possible measurement as a deterministic pair. The frequency degree of freedom comprises just one two dimensional basis, not the two, two dimensional bases of polarization. In other words, the frequency degree of freedom is not as intrinsically secure as polarization degrees of freedom for random number generation utilized in quantum cryptography.
When congruent frequency f1 and incongruent frequency f2 are both horizontally polarized, transit through the birefringent stack 10 leaves the congruent frequency polarization intact, but rotates the incongruent frequency by 90°, to a vertical polarization state. Or, if the two photons are vertically polarized, again, the congruent frequency photon's polarization state is left intact, remaining vertical, but the incongruent photon's polarization state is rotated from vertical to horizontal polarization. The joint probability amplitude exiting the polarization beam splitter 20, and thus the hyperspectral filter stage 30 becomes,
                                                                    Γ              ⁡                              (                                                      f                    1                                    ;                                      f                    2                                                  )                                      〉                    out                =                              1                          2                                ⁢                      (                                                                                                f                    1                                    ,                                      H                    1                                    ,                                                            P                      2                                        ;                                          f                      2                                                        ,                                      V                    2                                    ,                                      P                    3                                                  〉                            +                                                                                    f                    1                                    ,                                      V                    1                                    ,                                                            P                      3                                        ;                                          f                      2                                                        ,                                      H                    2                                    ,                                      P                    2                                                  〉                                      )                                              (        2        )            Transiting the polarization beam splitter 20, the two photons are directed into two orthogonal directions. The polarization beam splitter 20 is a projection operator. Horizontal polarizations exit P3 in FIG. 1 and vertical polarizations exit P2. Polarization measurements of a photon exiting P3 are no longer randomly distributed, nor are polarization measurements exiting P2. Thus, the polarization randomness of the input state given in equation (1) is lost upon projection and subsequent measurement. In terms of information utility, they behave like the frequency behaves prior to entering the hyperspectral filter stage 30 i.e., like one two dimensional basis without randomness. Frequency measurements, however, are random. After transiting the hyperspectral filter stage 30, they can provide anti-correlated random bit streams at either port. If the output of P2 is f1, the output of P3 is f2, and vice versa.
Useful polarization entanglement is lost and replaced by less useful frequency entanglement. The difference in utility is the fact that polarization entanglement allows for measuring in at least two, two dimensional bases, while frequency entanglement allows measurement in only one two dimensional basis. For quantum key distribution purposes, two non-orthogonal two dimensional bases allow ambiguity in an eavesdropper's interpretation of the logical meaning of their measurements. One two dimensional frequency basis does not allow such ambiguity to be imparted to an eavesdropper. It is therefore desirable to modify the single hyperspectral filter stage 30 to recover the more intrinsically secure polarization entanglement.